Operation Of Integer Rules

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Complete the following questions by filling in the missing information in the blank that best completes the statement.

• 1.

Explanation
When adding like signs in addition, you should add and keep the sign. This means that if both numbers being added have the same sign (either positive or negative), the sum will also have the same sign. For example, if you add two positive numbers or two negative numbers, the sum will be positive.

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• 2.

When multiplying a ______________________________ factor with a negative factor, your product will be a positive.

Explanation
When multiplying a negative factor with a negative factor, the two negatives cancel each other out, resulting in a positive product. This is because multiplying two negative numbers together is equivalent to multiplying their absolute values and then making the product positive.

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• 3.

When subtracting integers, you must ______________________________________ the sign of the subtrahend, change the operation's sign to addition, and then follow the rules for addition of integers.

Explanation
When subtracting integers, you must change the sign of the subtrahend, change the operation's sign to addition, and then follow the rules for addition of integers. This is because subtracting a number is the same as adding its opposite. By changing the sign of the subtrahend and the operation, we can convert the subtraction problem into an addition problem and then apply the rules for adding integers.

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• 4.

When adding ______________________________________ signs in addition, you should subtract and keep the sign of the larger number.

Explanation
When adding numbers with different signs, the rule is to subtract the smaller number from the larger number and keep the sign of the larger number. This is because when we subtract a smaller number, it is essentially adding a negative value. Therefore, the answer will have the sign of the larger number.

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• 5.

When dividing a negative integer by a ___________________________________ integer, your quotient will result as a negative.

Explanation
When dividing a negative integer by a positive integer, the quotient will result as a negative. This is because when we divide a negative number by a positive number, the result is always negative. For example, if we divide -10 by 2, the quotient is -5. This is because dividing a negative number into equal parts will always result in a negative value.

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• 6.

When multiplying a negative factor with a positive factor, your product will result in a ________________________________________.

Explanation
When multiplying a negative factor with a positive factor, your product will result in a negative value. This is because when you multiply a positive number by a negative number, the result is always negative.

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• 7.

When dividing a positive integer with a positive integer, you quotient will be a _________________________________________.

Explanation
When dividing a positive integer with a positive integer, the quotient will always be positive. This is because dividing a positive number by another positive number will result in a smaller positive number or zero. The division operation represents the distribution of the dividend into equal parts, and since both numbers are positive, there will always be a positive number of parts. Therefore, the quotient will be positive.

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• 8.

6 + (-2) = -4

• A.

True

• B.

False

B. False
Explanation
The given equation states that 6 plus negative 2 equals negative 4. However, this is incorrect. The correct answer is that 6 plus negative 2 equals 4.

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• 9.

4 x (-4) = -16

• A.

True

• B.

False

A. True
Explanation
The given equation is a simple multiplication problem. When you multiply 4 by -4, the result is -16. Therefore, the statement "4 x (-4) = -16" is true.

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• 10.

5 - (-4) = 9

• A.

True

• B.

False

A. True
Explanation
When subtracting a negative number, it is equivalent to adding the positive value of that number. In this case, subtracting -4 is the same as adding 4. Therefore, 5 - (-4) becomes 5 + 4, which equals 9. Hence, the statement is true.

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• 11.

-15-5   = -3

• A.

True

• B.

False

B. False
Explanation
The given equation is -15-5 = -3. However, this equation is not true because the sum of -15 and -5 is -20, not -3. Therefore, the correct answer is False.

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• 12.

(-1) + (-13) = -12

• A.

True

• B.

False

B. False
Explanation
The given equation is (-1) + (-13) = -14, not -12. Therefore, the correct answer is False.

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• 13.

(-5) - (-3) = -8

• A.

True

• B.

False

B. False
Explanation
The given equation is (-5) - (-3) = -8. By subtracting a negative number, it becomes equivalent to adding a positive number. Therefore, (-5) - (-3) is the same as (-5) + 3, which equals -2. Since -2 is not equal to -8, the answer is False.

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• 14.

4020 = 2

• A.

True

• B.

False

A. True
Explanation
The given statement "4020 = 2" is false. The equation states that the number 4020 is equal to 2, which is not true. Therefore, the correct answer is False.

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• 15.

(-5)(-5) = 25

• A.

True

• B.

False

A. True
Explanation
The given equation (-5)(-5) = 25 is true because when two negative numbers are multiplied, the result is always positive. In this case, multiplying -5 by -5 gives us 25, which is a positive number. Therefore, the answer is true.

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• 16.

-41 - 19 = 22

• A.

True

• B.

False

B. False
Explanation
The given equation is -41 - 19 = 22. However, this equation is incorrect. When we subtract 19 from -41, the result is -60, not 22. Therefore, the correct answer is False.

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